2.2.23改进。用实验评估正文中所提到的归并排序的三项改进(请见练习2.2.11)的效果,并比较正文中实现的归并和练习2.2.10所实现的归并之间的性能。根据经验给出应该在何时为子数组切换到插入排序。
3)根据经验给出应该在何时为子数组切换到插入排序。
依据下图的试验结果,得出子数组长度在16至18时适合切换到插入排序。
public class E2d2d23d3
{
public static double time (Double[] a,int subArrayLenTrunONInsertionSort)
{
Stopwatch timer =new Stopwatch();
E2d2d11d3.sort(a,subArrayLenTrunONInsertionSort);
return timer.elapsedTime();
}
public static double timeRandomInput(int N,int T,int subArrayLenTrunONInsertionSort)
{
double total =0.0;
Double[] a=new Double[N];
for (int t=0;t<T;t++)
{
for (int i=0;i<N;i++)
a[i]=StdRandom.uniform();
total+=time(a,subArrayLenTrunONInsertionSort);
}
return total/T;
}//end timeRandomInput
public static void main(String[] args)
{
int N=Integer.parseInt(args[0]);
int T=Integer.parseInt(args[1]);
int maxInsertLen=Integer.parseInt(args[2]);
StdOut.printf("For %d random Doubles %d times sort ",N,T);
for (int i=1;i<=maxInsertLen;i++)
{
double t=timeRandomInput(N,T,i);
StdOut.printf("subArrayLenTrunONInsertionSort=%d spend time=%.2f ",i,t);
}
}
}
public class E2d2d11d3
{
public static void sort(Comparable[] a,int subArrayLenTrunONInsertionSort)
{
int len=a.length;
Comparable[] aux=new Comparable[len];
for(int i=0;i<len;i++)
aux[i]=a[i];
sort(a,aux,0,a.length-1,subArrayLenTrunONInsertionSort);
}
private static void sort(Comparable[] a,Comparable[] aux,int lo,int hi,int subArrayLenTrunONInsertionSort)
{
if ((hi-lo+1)<=subArrayLenTrunONInsertionSort)
{
insertionSort(a,lo,hi);
}
else
{
int mid=lo+(hi-lo)/2;
sort(aux,a,lo,mid,subArrayLenTrunONInsertionSort);
sort(aux,a,mid+1,hi,subArrayLenTrunONInsertionSort);
if(!less(aux[mid+1],aux[mid]))
{
for(int i=lo;i<=hi;i++)
a[i]=aux[i];
return;
}
merge(aux,a,lo,mid,hi);
}
}
private static void merge(Comparable[] a,Comparable[] aux,int lo,int mid,int hi)
{
int i=lo;
int j=mid+1;
for(int k=lo;k<=hi;k++)
{
if (i>mid) aux[k]=a[j++];
else if (j>hi) aux[k]=a[i++];
else if (less(a[j],a[i])) aux[k]=a[j++];
else aux[k]=a[i++];
}
}
private static boolean less(Comparable v,Comparable w)
{ return v.compareTo(w)<0;}
private static void exch(Comparable[] a,int i,int j)
{
Comparable t=a[i];
a[i]=a[j];
a[j]=t;
}
private static void insertionSort(Comparable[] a,int lo,int hi)
{
for (int i=lo+1;i<=hi;i++)
for (int j=i;j>lo && less(a[j],a[j-1]);j--)
exch(a,j,j-1);
}
public static boolean isSorted(Comparable[] a)
{
for(int i=1;i<a.length;i++)
if(less(a[i],a[i-1])) return false;
return true;
}
}
3)根据经验给出应该在何时为子数组切换到插入排序。
依据下图的试验结果,得出子数组长度在16至18时适合切换到插入排序。
public class E2d2d23d3
{
public static double time (Double[] a,int subArrayLenTrunONInsertionSort)
{
Stopwatch timer =new Stopwatch();
E2d2d11d3.sort(a,subArrayLenTrunONInsertionSort);
return timer.elapsedTime();
}
public static double timeRandomInput(int N,int T,int subArrayLenTrunONInsertionSort)
{
double total =0.0;
Double[] a=new Double[N];
for (int t=0;t<T;t++)
{
for (int i=0;i<N;i++)
a[i]=StdRandom.uniform();
total+=time(a,subArrayLenTrunONInsertionSort);
}
return total/T;
}//end timeRandomInput
public static void main(String[] args)
{
int N=Integer.parseInt(args[0]);
int T=Integer.parseInt(args[1]);
int maxInsertLen=Integer.parseInt(args[2]);
StdOut.printf("For %d random Doubles %d times sort ",N,T);
for (int i=1;i<=maxInsertLen;i++)
{
double t=timeRandomInput(N,T,i);
StdOut.printf("subArrayLenTrunONInsertionSort=%d spend time=%.2f ",i,t);
}
}
}
public class E2d2d11d3
{
public static void sort(Comparable[] a,int subArrayLenTrunONInsertionSort)
{
int len=a.length;
Comparable[] aux=new Comparable[len];
for(int i=0;i<len;i++)
aux[i]=a[i];
sort(a,aux,0,a.length-1,subArrayLenTrunONInsertionSort);
}
private static void sort(Comparable[] a,Comparable[] aux,int lo,int hi,int subArrayLenTrunONInsertionSort)
{
if ((hi-lo+1)<=subArrayLenTrunONInsertionSort)
{
insertionSort(a,lo,hi);
}
else
{
int mid=lo+(hi-lo)/2;
sort(aux,a,lo,mid,subArrayLenTrunONInsertionSort);
sort(aux,a,mid+1,hi,subArrayLenTrunONInsertionSort);
if(!less(aux[mid+1],aux[mid]))
{
for(int i=lo;i<=hi;i++)
a[i]=aux[i];
return;
}
merge(aux,a,lo,mid,hi);
}
}
private static void merge(Comparable[] a,Comparable[] aux,int lo,int mid,int hi)
{
int i=lo;
int j=mid+1;
for(int k=lo;k<=hi;k++)
{
if (i>mid) aux[k]=a[j++];
else if (j>hi) aux[k]=a[i++];
else if (less(a[j],a[i])) aux[k]=a[j++];
else aux[k]=a[i++];
}
}
private static boolean less(Comparable v,Comparable w)
{ return v.compareTo(w)<0;}
private static void exch(Comparable[] a,int i,int j)
{
Comparable t=a[i];
a[i]=a[j];
a[j]=t;
}
private static void insertionSort(Comparable[] a,int lo,int hi)
{
for (int i=lo+1;i<=hi;i++)
for (int j=i;j>lo && less(a[j],a[j-1]);j--)
exch(a,j,j-1);
}
public static boolean isSorted(Comparable[] a)
{
for(int i=1;i<a.length;i++)
if(less(a[i],a[i-1])) return false;
return true;
}
}